You are correct. PP's mathematician was making a bold psychological/sociological claim. Maybe he has seen some research to that effect, but I doubt it.
Yes, of course he knew that all occurrences are equally probable, but he took into consideration what other people bet. Anyway as I remember when asked about that strategy few years later he said he changed the sequence (to 2,3,4,5,6,7 or something similar) to avoid potential prize sharing with people who followed his advice.